Hi,
In an old company standard i saw this prescribed method for computing UCL for P-charts.

UCL = AVERAGE(p) + 3*Sigma(p)

where p is the defect rate per subgroup (so they are getting stdev(defect rates)). It further explains that it is the direct use of the basic formula mean +/- 3*sigma.

Now i dont have an issue with the direct formula. But somewhat i know that this method to estimate the sigma is wrong. I have only seen two methods to compute the control limits for p-charts, namely use sigma estimate of p*q/n, and the use of moving range. How do i explain in layman's term then that the old company standard is wrong? They do sure claim that it worked in the past...

Any comments, folks?

I'm not sure I would say they are wrong ...

The p chart typically assumes that the data comes from a binomial distribution. And for a binomial distribution, the standard deviation is (p*q/n)^1/2.

So you should be able to write equally well

UCL = AVERAGE(p) + 3*Sigma(p)

or

UCL = AVERAGE(p) + 3*(p*q/n)^1/2

The second is much easier to calculate "by hand" - once you have p = proportion defective you can easily find (p*q/n)^0.5 in 10 seconds on a pocket calculator.

Now, I should say that (p*q/n)^1/2 and Sigma(p) are slightly different ways to get the standard deviation, so they will give slightly different values. A quick simulation shows that sometimes one is a little higher and sometimes the other is a little higher, but they are always in the same ballpark. Thus either one should work. (If the data do not indeed follow the binomial distribution, the two method could give noticeably different results.)



And if you like quoting an authority, Pyzdek in his Quality Engineering Handbook says "Like all control charts, p charts consist of three guidelines: center line, a lower control limit, and an upper control limit. The center line is the average proportion defective and the two control limits are set at plus and minus three standard deviations." He then goes on to say you would calculate the standard deviation using (p*q/n)^1/2.

Any other comments or interpretations?


Tim F

Thanks, Tim!

And if you like quoting an authority, Pyzdek in his Quality Engineering Handbook says "Like all control charts, p charts consist of three guidelines: center line, a lower control limit, and an upper control limit.

Did Tom really say that? For shame. I will give him a lower control limit, and an upper control limit...but not center line. :tg:

Did Tom really say that? For shame. I will give him a lower control limit, and an upper control limit...but not center line. :tg:

What would you called the average percent defective? If not the center line?

What would you called the average percent defective? If not the center line?


That wasn't the part I was disagreeing about - it was the "Like all control charts"...and center lines. :tg: